The packaging of annular objects such as automobile tires in thermoplastic synthetic resin foils presents some difficulty. Firstly it has been found to be extremely handy to have the packaging material follow the annular shape of the tire, with a hole in the center i.e. to hug the inner and outer periphery of the packaged object for easiest handling and transport. The removal of the center web, however, is fraught with difficulties since it must be done with accuracy and at the same time rapidly, in the course of production.